In County X, 60 percent of the households have an annual income of

Question

In County X, 60 percent of the households have an annual income of more than $25,000. If 95 percent of the households in the county have annual incomes below $100,000, and if 3,000 households have annual incomes of at least $100,000, then how many households in County X have annual incomes between $25,000 and $100,000, noninclusive?

(A) 12,000
(B) 24,000
(C) 33,000
(D) 36,000
(E) 60,000

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

finner999 · Answer

6o% of HH have  more than  25.000$ income
95% of HH have  less than  100.000$ income
 -> 3.000 HH have income of  at least  100.000$
 -> Difference: 100%-95%=5% -> 3.000 HH equal 5% of the entirety, 6.000HH = 10%
95% (HH below 100.000$)-40% (HH below 25.000$) = 55% between 100.000$ and 25.000$
5,5*6.000HH= 33.000

Hence Answer C  should be  correct.

ADisHere · Answer

5% have more than 1 lakh -> 3000 households
so 100% should be in all 60000 households

of that 60% have more than 25k income so 36000 households, but we need to exclude 5% have more than 1 lakh -> 3000 households
So 36k-3k= 33k
Hence C

giuseppemvn · Answer

Question asks for households in County X with income from 25k to 100k non-inclusive.

Since we know that: 
- 60% of X have more than 25k => We have to take 60% of the number of households in X and subtract the percentage of households that have more than 100k to answer the question.

We also know that: 
- 95% of X have less than 100k => This means that 5% have more than 100k. Therefore we need 55% of total households in X to solve the problem.

- 3000 households have at least 100k => We then know that 5% of X is 3000. If we solve the equation we get X = 60k.

Final passage: 55% of X = 55% of 60,000 = 33,000.

Answer C

sushanth21 · Answer

95% earn less than 100,000
5% earn more than 100,000
5%x = 3000
x = 60000
to find between 25000 and 100000
remove the households that earn more than 100000 from the households tahth earn more than 25000
60%x - 5%x = 55%x
0.55 * 60000 = 33000

arkadutt · Answer

Detailed explanation (or, how I worked through this problem)

60% of households have annual incomes of more than $25,000. 
 95% of households have annual incomes of less than $100,000. 
 60% of households have incomes of more than $25,000  
5% of households (100%−95%) have annual incomes of at least $100,000, which equals 3,000 households.
 Let the total number of households be H. Since 5% of H equals 3,000 i.e. 0.05H=3000. 
Then, H =  60,000

Number of households with income over $25k  
Thus, 0.6H=0.6×60,000= 36,000

Also, the number of households with incomes below $100k
95% of households have incomes of less than $100,000:
0.95H=0.95×60,000= 57,000

Households with incomes more than $25,000 but less than $100,000 are :  
Households between 25,000 and 100,000=57,000−(60,000−36,000) =  33,000

In County X, 60 percent of the households have an annual income of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In County X, 60 percent of the households have an annual income of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards